Congruences modulo powers of 7 for k-elongated plane partitions

2025/08/13 by Chen, Dandan, Xu, Tianjian, Yin, Siyu · 1 citation
#05A17 #11P83 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.09723

Abstract

The enumeration d_k(n) of k-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function p(n). Congruences for d_k(n) modulo certain powers of primes have been proven via elementary means and modular forms by many authors. Recently, Banerjee and Smoot established an infinite family of congruences for d₅(n) modulo powers of 5. In this paper we have discovered an infinite congruence family for d₃(n) and d₅(n) modulo powers of 7.

Citations

• Congruences modulo powers of 5 and 7 for the crank and rank parity functions and related mock theta functions
• 2-Elongated Plane Partitions and Powers of 7: The Localization Method Applied to a Genus 1 Congruence Family
• The Localization Method Applied to k-Elongated Plane Partitions and Divisibility by 5
• Congruences for k-elongated plane partition diamonds
• MacMahon's partition analysis XIII: Schmidt type partitions and modular forms
• A tutorial for the MAPLE ETA package

Cited by

• Congruences modulo 7 and 11 for certain two restricted partition functions

Related

• The k-elongated plane partition function modulo small powers of 5
• On the Divisibility of 7-Elongated Plane Partition Diamonds by Powers of 8
• The Localization Method Applied to k-Elongated Plane Partitions and Divisibility by 5
• Congruences modulo 7 and 11 for certain two restricted partition functions
• Congruences for k-elongated plane partition diamonds